Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 1 Chapter 13 Equity Valuation

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 2 Fundamental Stock Analysis: Models of Equity Valuation Basic Types of Models –Balance Sheet Models –Dividend Discount Models –Price/Earning Ratios Estimating Growth Rates and Opportunities

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 3 Intrinsic Value and Market Price Intrinsic Value –Self assigned Value –Variety of models are used for estimation Market Price –Consensus value of all potential traders Trading Signal –IV > MP Buy –IV < MP Sell or Short Sell –IV = MP Hold or Fairly Priced

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 4 Dividend Discount Models: General Model V 0 = Value of Stock D t = Dividend k = required return

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 5 No Growth Model Stocks that have earnings and dividends that are expected to remain constant Preferred Stock

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 6 No Growth Model: Example E 1 = D 1 = $5.00 k =.15 V 0 = $5.00 /.15 = $33.33

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 7 Constant Growth Model g = constant perpetual growth rate

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 8 Constant Growth Model: Example E 1 = $5.00b = 40% k = 15% (1-b) = 60%D 1 = $3.00 g = 8% V 0 = 3.00 / ( ) = $42.86

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 9 Estimating Dividend Growth Rates g = growth rate in dividends ROE = Return on Equity for the firm b = plowback or retention percentage rate – (1- dividend payout percentage rate)

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 10 Shifting Growth Rate Model g 1 = first growth rate g 2 = second growth rate T = number of periods of growth at g 1

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 11 Shifting Growth Rate Model: Example D 0 = $2.00 g 1 = 20% g 2 = 5% k = 15% T = 3 D 1 = 2.40 D 2 = 2.88 D 3 = 3.46 D 4 = 3.63 V 0 = D 1 /(1.15) + D 2 /(1.15) 2 + D 3 /(1.15) 3 + D 4 / ( ) ( (1.15) 3 V 0 = = $30.40

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 12 Specified Holding Period Model P N = the expected sales price for the stock at time N N = the specified number of years the stock is expected to be held

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 13 Partitioning Value: Growth and No Growth Components PVGO = Present Value of Growth Opportunities E 1 = Earnings Per Share for period 1

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 14 Partitioning Value: Example ROE = 20% d = 60% b = 40% E 1 = $5.00 D 1 = $3.00 k = 15% g =.20 x.40 =.08 or 8%

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 15 Partitioning Value: Example V o = value with growth NGV o = no growth component value PVGO = Present Value of Growth Opportunities

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 16 Price Earnings Ratios P/E Ratios are a function of two factors –Required Rates of Return (k) –Expected growth in Dividends Uses –Relative valuation –Extensive Use in industry

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 17 P/E Ratio: No expected growth E 1 - expected earnings for next year –E 1 is equal to D 1 under no growth k - required rate of return

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 18 P/E Ratio with Constant Growth b = retention ration ROE = Return on Equity

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 19 Numerical Example: No Growth E 0 = $2.50 g = 0 k = 12.5% P 0 = D/k = $2.50/.125 = $20.00 PE = 1/k = 1/.125 = 8

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 20 Numerical Example with Growth b = 60% ROE = 15% (1-b) = 40% E 1 = $2.50 (1 + (.6)(.15)) = $2.73 D 1 = $2.73 (1-.6) = $1.09 k = 12.5% g = 9% P 0 = 1.09/( ) = $31.14 PE = 31.14/2.73 = 11.4 PE = (1 -.60) / ( ) = 11.4